# Fermion-scalar conformal blocks

@article{Iliesiu2015FermionscalarCB, title={Fermion-scalar conformal blocks}, author={Luca V. Iliesiu and Filip Kos and David Poland and Silviu S. Pufu and David Simmons-Duffin and Ran Yacoby}, journal={Journal of High Energy Physics}, year={2015}, volume={2016}, pages={1-20} }

A bstractWe compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called ‘seed blocks’ in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators.

## 76 Citations

### Multipoint conformal blocks in the comb channel

- MathematicsJournal of High Energy Physics
- 2019

A bstractConformal blocks are the building blocks for correlation functions in conformal field theories. The four-point function is the most well-studied case. We consider conformal blocks for…

### Conformal correlators and blocks with spinors in general dimensions

- Mathematics
- 2017

We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac…

### Dimensional reduction for conformal blocks

- Mathematics
- 2016

A bstractWe consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d + 1, 1) up into multiplets of SO(d, 1). This leads to an expansion of…

### Counting conformal correlators

- Mathematics
- 2016

A bstractWe introduce simple group-theoretic techniques for classifying conformallyinvariant tensor structures. With them, we classify tensor structures of general n-point functions of non-conserved…

### Harmony of spinning conformal blocks

- Mathematics
- 2016

A bstractConformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning…

### Weight shifting operators and conformal blocks

- Mathematics
- 2017

A bstractWe introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving…

### Fermion conformal bootstrap in 4d

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE…

### Conformal four-point correlation functions from the operator product expansion

- MathematicsJournal of High Energy Physics
- 2020

Abstract
We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in [1, 2] and present several explicit examples of blocks derived via…

### Bootstrapping 3D fermions with global symmetries

- Mathematics
- 2017

A bstractWe study the conformal bootstrap for 4-point functions of fermions 〈ψiψjψkψℓ〉 in parity-preserving 3d CFTs, where ψi transforms as a vector under an O(N ) global symmetry. We compute bounds…

### Radial expansion for spinning conformal blocks

- Mathematics
- 2016

A bstractThis paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the…

## References

SHOWING 1-10 OF 61 REFERENCES

### Bootstrapping 3D fermions

- Physics
- 2015

A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in…

### Deconstructing conformal blocks in 4D CFT

- Mathematics
- 2015

A bstractWe show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field…

### Recursion relations for conformal blocks

- Mathematics
- 2015

A bstractIn the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension Δ of the…

### Scalar-vector bootstrap

- Mathematics
- 2015

A bstractWe work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field…

### Central charge bounds in 4D conformal field theory

- Computer Science
- 2011

It is shown that the stress tensor central charge C-T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory.

### Radial Coordinates for Conformal Blocks

- Mathematics
- 2013

We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is…

### Projectors, shadows, and conformal blocks

- Mathematics
- 2014

A bstractWe introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to…

### Bootstrapping the 3d Ising twist defect

- Physics, Mathematics
- 2014

A bstractRecent numerical results point to the existence of a conformally invariant twist defect in the critical 3d Ising model. In this note we show that this fact is supported by both epsilon…

### The superconformal bootstrap for structure constants

- Mathematics
- 2014

A bstractWe report on non-perturbative bounds for structure constants on N=4$$ \mathcal{N}=4 $$ SYM. Such bounds are obtained by applying the conformal bootstrap recently extended to super-conformal…

### Bootstrapping the Three Dimensional Supersymmetric Ising Model.

- PhysicsPhysical review letters
- 2015

The conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry is implemented and universal constraints on the spectrum of operator dimensions in these theories are found.